3. Consider the following two assets. Returns on asset 1 have a mean of 15% and a standard deviation of 20%. Returns on asset 2 have a mean of 8% and a standard deviation of 10%. The correlation coefficient 1,2 measures how the two assets returns are correlated, and it takes on values between -1 and +1. An investor puts W1 fraction of her wealth into stock 1, and W2 = 1 W1 fraction of her wealth into stock 2.

a. When 1,2 = 1, argue using mathematical formulas that the portfolio standard deviation is equal to the weighted average of the standard deviation of the individual stocks in the portfolio. (Hint, Square of Summation)

b. Now suppose 1,2 = 1. If the investor wants to minimize her risk in investing in this portfolio, how should she choose W1 and W2 = 1 W1? (Hint, Square of Difference).

c. Suppose 1,2 = 0.25. What is the expected return and the standard deviation of your portfolio when you set W1 = 0.4 and W2 = 1 W1 = 1 0.4 = 0.6?